We investigate the form of structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to recent criticisms, and our view is that the problems raised stem from the lack of proper, mathematics-free theoretical foundations. We attempt to provide such foundations and show that our foundations have consequences, in the form of theorems, that provide answers to the main questions and problems that have arisen in connection with this form of structuralismn. Our solutions to the problems of structuralism are not developed piecemeal but rather justified by reference to a principled position.